Yes, assuming he has an android phone with a data plan rooting the phone is the best option. Both my tablet and phone are rooted and I have a ROM on my phone that enables WiFi tethering. However, my understanding of the recent FCC finding against Verizon is that neither need to be --rooted to do this.
If I understand what the OP is saying the problem is that the tethering app he has chosen to use only allows him to use Bluetooth to connect the tablet to his phone. I would recommend that the OP investigate a different app to use for tethering instead of rooting either of his devices. To me it sounds more like a configuration problem with the app he is using to tether. I have had the most success tethering by disabling wifi security options while tethering. Without knowing what phone the OP has there is not much more to recommend.
